I’d definitely recommend steel for road fixed. The frame is noticeably less rigid than my alloy and carbon bikes. You spend a lot of time out of the saddle (if you ride a big gear), and like a SS mtb, the flex does help with comfort. As for geometry; 73 degrees parallel suits my road bike. My steel track bike is a steep 74.5 and this is not a nice bike for the road. Some of the Genesis bikes have slacker geometry, and whilst relaxing, doesn’t give that really nice road bike handling.
An old 531 frame (not 501) would be a good choice, but the bearings may all be rubbish, and you might need new tools to fix and replace. Watch for a siezed seatpost too. The Fuji is a good place to start, but off the peg they are heavy. I’d still look for a used Paddy Wagon. There’s a 2015 56cm on the bay for £185 at the moment. A new set of wheels, or just a back wheel would get you within budget.
Wheels are ALWAYS the best upgrade here, for some reason, cheap, heavy large flange, pseudo track wheels are the norm. A proper set of road wheels with a fixed hub is a much nicer prospect. Just commuted 15 miles on mine on 25c Vittoria Paves, just a lovely ride, regardless of whether fixed. It always makes me smile.